正子斷層掃描影像的實證研究及混合型加速的GEM演算法

Abstract

中文摘要 由於資料的不完整及隨機性質，對於正子斷層掃描影像(PET)的重建是一件很困難的工作。利用EM 演算法求得最大概似估計量(MLE) 以重建正子斷層掃描影像強度是文獻上建議的方法。此種方法具有列運算、線性複雜度、單調收斂性、非負解以及可平行化的特性。針對台北榮民總醫院的PET系統，我們進行實證研究，比較由MLE-EM演算法及仍在商業系統上運用的FBP (Filtered Backprojection) 演算法所重建的影像，並進一步設計實驗來估計隨機偶合事件 (Random Coincidence Events)。 但是EM演算法的收斂速度慢，故文獻上己有數種不同的加速方法。例如：SAGE、AECM等方法，進一步改變完整資料空間的選擇，以加快收斂速度，同時保持一些EM演算法的優點。可是這些方法郤無法平行化，因此我們提出混合型加速的GEM演算法，同時保持EM演算法的特性，更可以加快收斂速度及進行平行化。本篇論文研究HSAGE、HEM (Hybrid SAGE、 Hybrid EM) 演算法，並應用在實證的資料上。

Abstract: The reconstruction of a medical image in positron emission tomography (PET) is difficult due to the indirect and random observations in a large system. The maximum likelihood estimate with the EM algorithm (MLE-EM) was proposed in literature to reconstruct the intensity of positron emission of PET with the merits of row operation, linear complexity, monotonic convergence, nonnegativeness, and parallelizability. Based on the empirical studies of the Veterans General Hospital (V.G.H.)-Taipei PET system, we will compare the reconstruction results of the MLE-EM with those of filtered backprojection (FBP) that are routinely used in commercial systems. Furthermore, experiments are designed to explore the random coincidence events by the MLE-EM. One of the disadvantages about EM algorithm is its slow convergence speed. Various accelerated methods had been proposed in literature, like the space-alternating generalized expectation maximization (SAGE) or the alternative expectation/conditional maximization (AECM) algorithms. They preserve the merits of row operation, linear complexity, monotonic convergence, and nonnegativeness. But they are not parallelizable. Combined with the search along the generalized gradient direction that increases the incomplete space log-likelihood, hybrid accelerators can further improve the convergence speeds of these generalized EM algorithms. Meanwhile, all the merits of the generalized EM algorithms are preserved. The resulting new algorithms, include the hybrid EM and hybrid SAGE (or hybrid AECM) algorithms, are studied based on the empirical data in this thesis.